Fix flickering in embedded game when paused

[Hilderin]

• Fixes Horrible Flickering when closing docks while embedded game is paused #101993

This PR should fix the flickering and artefacts when the embedded game is resized for a larger size when the game is paused. This is caused by the fact that Godot does not rerender when the game is paused, which is expected.

Although I was unable to reproduce the flickering on my computer, I did observe artifacts when the game was paused and the window was resized to a larger size.

To prevent these artifacts and hopefully the flickering, I have implemented a solution that saves the size of the embedded game when the pause is activated. This saved size is then set as a fixed size in the embedded process control to ensure the game window never becomes larger.

I also fixed another issue related to pause mode. When the game was paused, closing the floating window did not complete until the game was unpaused. This issue occurred because the close message sent to the window was not processed.

Additionally, I discovered another minor, unrelated issue. If the last selected tab was Game when the editor was launched, and the game was started with the floating window enabled, a blank main screen would appear in the editor. The content of the Game tab was transferred to the floating window, but the tab (main screen) was not changed for another editor.

[bruvzg]

Was not able to reproduce the flickering, but changes look reasonable, and I have not encountered any issues while testing it.

[Repiteo]

Thanks!

[JekSun97]

@Hilderin Unfortunately the problem still appears, I noticed that this problem only occurs when running a 2D scene, when running a 3D scene I can't produce the problem, to check this, run a 2D scene, press pause, minimize the editor window, and expand, you should see a black square that is not cleared.